If
then
Where r= remainder This makes no since to me. some function divided by x-k yields the function of k.

This statement is deduced based on the Polynomial Remainder Theorem. That is, if you have a function , and you divide it with another function , then the remainder of the division is equals to . Proof:

Let's say you have a function , where is the quotient (the result of dividing with ) and is the remainder (after dividing with ). According to the Polynomial Division Algorithm, the remainder of the division must have a smaller degree than the divisor, in this case, . Since has a degree of 1, must be a constant polynomial.